Author: Justin Holladay
Publisher: Createspace Independent Publishing Platform
ISBN: 9781539682394
Category :
Languages : en
Pages : 144
Book Description
Printable Middle School Math Games - Math Teachers, Look No Further! 42 printable math games for upper elementary and middles school students, easy-to-setup for any math class, when laminated these can be made into math board games for middle school that can be used over and over again. WHAT IS A MATH FILE FOLDER GAME? A Math File Folder Game fits in a folder making it easy to use and ready at a moment's notice. Very few other items are required. You'll need to construct or reproduce the included game boards and have playing cards and dice handy. A few games use other types of geometric manipulatives that are standard items in most elementary and middle school classrooms. This value-packed book contains 42 math games that will give your students so much fun they'll forget they're actually learning mathematics! But don't be fooled. Just because games are exciting doesn't mean that they're not built upon solid educational benefits. Students will learn basic skills, problem solving, and critical thinking across a wide variety of mathematical topics: measurement, arithmetic, algebra, and geometry. Here are some of the specific topics covered: congruence, similarity, perimeter, area, volume, linear measurement in standard and metric units, generating and analyzing patterns and relationships, practice and strategy with the four basic operations, understanding of fractions, both equivalence and ordering, modeling with mathematics, relationships between 2-D and 3-D objects, probability models, greatest common factor, least common multiple, prime factorization, ratio, proportion, and percent, liquid volumes, classification of angles, graphing on a coordinate plane, complementary and supplementary angles, rules for divisibility, operations with integers and rational numbers, absolute value, integer exponents, radicals, one variable equations, Pythagorean Theorem, statistical variability and measures of central tendency Math File Folder Games also offer teachers another benefit. They align to the US Common Core Standards and Common Core Mathematical Practices. By using Math Games at home or in your classroom with your upper elementary, middle school, or high school kids, you can provide them with hours of fun-filled learning time. And the best part is you'll get into the spirit and enjoy yourself, too!
Math File Folder Games
Author: Justin Holladay
Publisher: Createspace Independent Publishing Platform
ISBN: 9781539682394
Category :
Languages : en
Pages : 144
Book Description
Printable Middle School Math Games - Math Teachers, Look No Further! 42 printable math games for upper elementary and middles school students, easy-to-setup for any math class, when laminated these can be made into math board games for middle school that can be used over and over again. WHAT IS A MATH FILE FOLDER GAME? A Math File Folder Game fits in a folder making it easy to use and ready at a moment's notice. Very few other items are required. You'll need to construct or reproduce the included game boards and have playing cards and dice handy. A few games use other types of geometric manipulatives that are standard items in most elementary and middle school classrooms. This value-packed book contains 42 math games that will give your students so much fun they'll forget they're actually learning mathematics! But don't be fooled. Just because games are exciting doesn't mean that they're not built upon solid educational benefits. Students will learn basic skills, problem solving, and critical thinking across a wide variety of mathematical topics: measurement, arithmetic, algebra, and geometry. Here are some of the specific topics covered: congruence, similarity, perimeter, area, volume, linear measurement in standard and metric units, generating and analyzing patterns and relationships, practice and strategy with the four basic operations, understanding of fractions, both equivalence and ordering, modeling with mathematics, relationships between 2-D and 3-D objects, probability models, greatest common factor, least common multiple, prime factorization, ratio, proportion, and percent, liquid volumes, classification of angles, graphing on a coordinate plane, complementary and supplementary angles, rules for divisibility, operations with integers and rational numbers, absolute value, integer exponents, radicals, one variable equations, Pythagorean Theorem, statistical variability and measures of central tendency Math File Folder Games also offer teachers another benefit. They align to the US Common Core Standards and Common Core Mathematical Practices. By using Math Games at home or in your classroom with your upper elementary, middle school, or high school kids, you can provide them with hours of fun-filled learning time. And the best part is you'll get into the spirit and enjoy yourself, too!
Publisher: Createspace Independent Publishing Platform
ISBN: 9781539682394
Category :
Languages : en
Pages : 144
Book Description
Printable Middle School Math Games - Math Teachers, Look No Further! 42 printable math games for upper elementary and middles school students, easy-to-setup for any math class, when laminated these can be made into math board games for middle school that can be used over and over again. WHAT IS A MATH FILE FOLDER GAME? A Math File Folder Game fits in a folder making it easy to use and ready at a moment's notice. Very few other items are required. You'll need to construct or reproduce the included game boards and have playing cards and dice handy. A few games use other types of geometric manipulatives that are standard items in most elementary and middle school classrooms. This value-packed book contains 42 math games that will give your students so much fun they'll forget they're actually learning mathematics! But don't be fooled. Just because games are exciting doesn't mean that they're not built upon solid educational benefits. Students will learn basic skills, problem solving, and critical thinking across a wide variety of mathematical topics: measurement, arithmetic, algebra, and geometry. Here are some of the specific topics covered: congruence, similarity, perimeter, area, volume, linear measurement in standard and metric units, generating and analyzing patterns and relationships, practice and strategy with the four basic operations, understanding of fractions, both equivalence and ordering, modeling with mathematics, relationships between 2-D and 3-D objects, probability models, greatest common factor, least common multiple, prime factorization, ratio, proportion, and percent, liquid volumes, classification of angles, graphing on a coordinate plane, complementary and supplementary angles, rules for divisibility, operations with integers and rational numbers, absolute value, integer exponents, radicals, one variable equations, Pythagorean Theorem, statistical variability and measures of central tendency Math File Folder Games also offer teachers another benefit. They align to the US Common Core Standards and Common Core Mathematical Practices. By using Math Games at home or in your classroom with your upper elementary, middle school, or high school kids, you can provide them with hours of fun-filled learning time. And the best part is you'll get into the spirit and enjoy yourself, too!
Math for Programmers
Author: Paul Orland
Publisher: Manning Publications
ISBN: 1617295353
Category : Computers
Languages : en
Pages : 686
Book Description
In Math for Programmers you’ll explore important mathematical concepts through hands-on coding. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you’ll master the key Python libraries used to turn them into real-world software applications. Summary To score a job in data science, machine learning, computer graphics, and cryptography, you need to bring strong math skills to the party. Math for Programmers teaches the math you need for these hot careers, concentrating on what you need to know as a developer. Filled with lots of helpful graphics and more than 200 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest programming fields. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology Skip the mathematical jargon: This one-of-a-kind book uses Python to teach the math you need to build games, simulations, 3D graphics, and machine learning algorithms. Discover how algebra and calculus come alive when you see them in code! About the book In Math for Programmers you’ll explore important mathematical concepts through hands-on coding. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you’ll master the key Python libraries used to turn them into real-world software applications. What's inside Vector geometry for computer graphics Matrices and linear transformations Core concepts from calculus Simulation and optimization Image and audio processing Machine learning algorithms for regression and classification About the reader For programmers with basic skills in algebra. About the author Paul Orland is a programmer, software entrepreneur, and math enthusiast. He is co-founder of Tachyus, a start-up building predictive analytics software for the energy industry. You can find him online at www.paulor.land. Table of Contents 1 Learning math with code PART I - VECTORS AND GRAPHICS 2 Drawing with 2D vectors 3 Ascending to the 3D world 4 Transforming vectors and graphics 5 Computing transformations with matrices 6 Generalizing to higher dimensions 7 Solving systems of linear equations PART 2 - CALCULUS AND PHYSICAL SIMULATION 8 Understanding rates of change 9 Simulating moving objects 10 Working with symbolic expressions 11 Simulating force fields 12 Optimizing a physical system 13 Analyzing sound waves with a Fourier series PART 3 - MACHINE LEARNING APPLICATIONS 14 Fitting functions to data 15 Classifying data with logistic regression 16 Training neural networks
Publisher: Manning Publications
ISBN: 1617295353
Category : Computers
Languages : en
Pages : 686
Book Description
In Math for Programmers you’ll explore important mathematical concepts through hands-on coding. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you’ll master the key Python libraries used to turn them into real-world software applications. Summary To score a job in data science, machine learning, computer graphics, and cryptography, you need to bring strong math skills to the party. Math for Programmers teaches the math you need for these hot careers, concentrating on what you need to know as a developer. Filled with lots of helpful graphics and more than 200 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest programming fields. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology Skip the mathematical jargon: This one-of-a-kind book uses Python to teach the math you need to build games, simulations, 3D graphics, and machine learning algorithms. Discover how algebra and calculus come alive when you see them in code! About the book In Math for Programmers you’ll explore important mathematical concepts through hands-on coding. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you’ll master the key Python libraries used to turn them into real-world software applications. What's inside Vector geometry for computer graphics Matrices and linear transformations Core concepts from calculus Simulation and optimization Image and audio processing Machine learning algorithms for regression and classification About the reader For programmers with basic skills in algebra. About the author Paul Orland is a programmer, software entrepreneur, and math enthusiast. He is co-founder of Tachyus, a start-up building predictive analytics software for the energy industry. You can find him online at www.paulor.land. Table of Contents 1 Learning math with code PART I - VECTORS AND GRAPHICS 2 Drawing with 2D vectors 3 Ascending to the 3D world 4 Transforming vectors and graphics 5 Computing transformations with matrices 6 Generalizing to higher dimensions 7 Solving systems of linear equations PART 2 - CALCULUS AND PHYSICAL SIMULATION 8 Understanding rates of change 9 Simulating moving objects 10 Working with symbolic expressions 11 Simulating force fields 12 Optimizing a physical system 13 Analyzing sound waves with a Fourier series PART 3 - MACHINE LEARNING APPLICATIONS 14 Fitting functions to data 15 Classifying data with logistic regression 16 Training neural networks
File Folder Games
Author: Karen Finch
Publisher:
ISBN: 9781594416583
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN: 9781594416583
Category :
Languages : en
Pages :
Book Description
Mathematics and Computation
Author: Avi Wigderson
Publisher: Princeton University Press
ISBN: 0691189137
Category : Computers
Languages : en
Pages : 434
Book Description
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Publisher: Princeton University Press
ISBN: 0691189137
Category : Computers
Languages : en
Pages : 434
Book Description
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Street-Fighting Mathematics
Author: Sanjoy Mahajan
Publisher: MIT Press
ISBN: 0262265591
Category : Education
Languages : en
Pages : 152
Book Description
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.
Publisher: MIT Press
ISBN: 0262265591
Category : Education
Languages : en
Pages : 152
Book Description
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.
3D Math Primer for Graphics and Game Development, 2nd Edition
Author: Fletcher Dunn
Publisher: CRC Press
ISBN: 1568817231
Category : Computers
Languages : en
Pages : 848
Book Description
This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves.
Publisher: CRC Press
ISBN: 1568817231
Category : Computers
Languages : en
Pages : 848
Book Description
This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves.
Mathematics and the Imagination
Author: Edward Kasner
Publisher: Courier Corporation
ISBN: 0486320278
Category : Mathematics
Languages : en
Pages : 402
Book Description
With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.
Publisher: Courier Corporation
ISBN: 0486320278
Category : Mathematics
Languages : en
Pages : 402
Book Description
With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.
Mathematics for Machine Learning
Author: Marc Peter Deisenroth
Publisher: Cambridge University Press
ISBN: 1108569323
Category : Computers
Languages : en
Pages : 392
Book Description
The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
Publisher: Cambridge University Press
ISBN: 1108569323
Category : Computers
Languages : en
Pages : 392
Book Description
The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
More Math Into LaTeX
Author: George Grätzer
Publisher: Springer Science & Business Media
ISBN: 0387688528
Category : Computers
Languages : en
Pages : 629
Book Description
This is the fourth edition of the standard introductory text and complete reference for scientists in all disciplines, as well as engineers. This fully revised version includes important updates on articles and books as well as information on a crucial new topic: how to create transparencies and computer projections, both for classrooms and professional meetings. The text maintains its user-friendly, example-based, visual approach, gently easing readers into the secrets of Latex with The Short Course. Then it introduces basic ideas through sample articles and documents. It includes a visual guide and detailed exposition of multiline math formulas, and even provides instructions on preparing books for publishers.
Publisher: Springer Science & Business Media
ISBN: 0387688528
Category : Computers
Languages : en
Pages : 629
Book Description
This is the fourth edition of the standard introductory text and complete reference for scientists in all disciplines, as well as engineers. This fully revised version includes important updates on articles and books as well as information on a crucial new topic: how to create transparencies and computer projections, both for classrooms and professional meetings. The text maintains its user-friendly, example-based, visual approach, gently easing readers into the secrets of Latex with The Short Course. Then it introduces basic ideas through sample articles and documents. It includes a visual guide and detailed exposition of multiline math formulas, and even provides instructions on preparing books for publishers.
More Math Into LaTeX
Author: George Grätzer
Publisher: Springer
ISBN: 3319237969
Category : Computers
Languages : en
Pages : 621
Book Description
For over two decades, this comprehensive manual has been the standard introduction and complete reference for writing articles and books containing mathematical formulas. If the reader requires a streamlined approach to learning LaTeX for composing everyday documents, Grätzer’s © 2014 Practical LaTeX may also be a good choice. In this carefully revised fifth edition, the Short Course has been brought up to date and reflects a modern and practical approach to LaTeX usage. New chapters have been added on illustrations and how to use LaTeX on an iPad. Key features: An example-based, visual approach and a gentle introduction with the Short Course A detailed exposition of multiline math formulas with a Visual Guide A unified approach to TeX, LaTeX, and the AMS enhancements A quick introduction to creating presentations with formulas From earlier reviews: Grätzer’s book is a solution. —European Mathematical Society Newsletter There are several LaTeX guides, but this one wins hands down for the elegance of its approach and breadth of coverage. —Amazon.com, Best of 2000, Editor’s choice A novice reader will be able to learn the most essential features of LaTeX sufficient to begin typesetting papers within a few hours of time... An experienced TeX user, on the other hand, will find a systematic and detailed discussion of LaTeX fea tures. —Report on Mathematical Physics A very helpful and useful tool for all scientists and engineers. —Review of Astronomical Tools
Publisher: Springer
ISBN: 3319237969
Category : Computers
Languages : en
Pages : 621
Book Description
For over two decades, this comprehensive manual has been the standard introduction and complete reference for writing articles and books containing mathematical formulas. If the reader requires a streamlined approach to learning LaTeX for composing everyday documents, Grätzer’s © 2014 Practical LaTeX may also be a good choice. In this carefully revised fifth edition, the Short Course has been brought up to date and reflects a modern and practical approach to LaTeX usage. New chapters have been added on illustrations and how to use LaTeX on an iPad. Key features: An example-based, visual approach and a gentle introduction with the Short Course A detailed exposition of multiline math formulas with a Visual Guide A unified approach to TeX, LaTeX, and the AMS enhancements A quick introduction to creating presentations with formulas From earlier reviews: Grätzer’s book is a solution. —European Mathematical Society Newsletter There are several LaTeX guides, but this one wins hands down for the elegance of its approach and breadth of coverage. —Amazon.com, Best of 2000, Editor’s choice A novice reader will be able to learn the most essential features of LaTeX sufficient to begin typesetting papers within a few hours of time... An experienced TeX user, on the other hand, will find a systematic and detailed discussion of LaTeX fea tures. —Report on Mathematical Physics A very helpful and useful tool for all scientists and engineers. —Review of Astronomical Tools